Exponential stability of nonlinear differential delay equations

Abstract The aim of this paper is to investigate the exponential stability of a nonlinear differential delay equation dot x (t) = ƒ(t,x(t),x(t − τ) ) Introduce the corresponding differential equation (without delay) dot y (t) = ƒ (t, y(t), y(t) ) and assume it is exponentially stable. It will be shown in this paper that the differential delay equation will remain exponentially stable provided the time lag τ is small enough.